{"paper":{"title":"Hochschild products and global non-abelian cohomology for algebras. Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2015-03-18T12:10:43Z","abstract_excerpt":"Let $A$ be a unital associative algebra over a field $k$, $E$ a vector space and $\\pi : E \\to A$ a surjective linear map with $V = {\\rm Ker} (\\pi)$. All algebra structures on $E$ such that $\\pi : E \\to A$ becomes an algebra map are described and classified by an explicitly constructed global cohomological type object ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$. Any such algebra is isomorphic to a Hochschild product $A \\star V$, an algebra introduced as a generalization of a classical construction. We prove that ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$ is the coproduct of all non-abelian cohom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05364","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}